Aalborg Universitet
The Influence of Time on Bearing Capacity of Driven Piles
Jensen, J. Lysebjerg; Augustesen, A.; Sørensen, Carsten Steen
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NGM 2004 : Proceedings of the 14th Nordic Geotechnical Meeting
Publication date:
2004
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Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Jensen, J. L., Augustesen, A., & Sørensen, C. S. (2004). The Influence of Time on Bearing Capacity of Driven
Piles. In H. Garin (Ed.), NGM 2004 : Proceedings of the 14th Nordic Geotechnical Meeting: Ystad, Sweden, 1921 May 2004. (3 : 2004 ed., Vol. 1, pp. 103-111). Linköping: Swedish Geotechnical Society. (SGF Report).
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The Influence of Time on the Bearing Capacity of Driven Piles
J. Lysebjerg Jensen
Aalborg University, Denmark, lyseb99@civil.auc.dk
A. Augustesen
Aalborg University, Department of Civil Engineering, Denmark, i5aa@civil.auc.dk
C. S. Sørensen
Aalborg University, Department of Civil Engineering, Denmark,i5css@civil.auc.dk
Abstract: In Danish engineering practice, one of the ways to determine the ultimate bearing capacity of an axially loaded pile is by means of geostatic formulas.
In the equation describing the contribution from the shaft friction to the total bearing capacity for piles located entirely or partly in clay, a regeneration factor appears. The regeneration factor accounts for effects of dissipation of pore pressure
due to pile driving and true time effects such as ageing on the ultimate bearing capacity. Normally the factor is 0.4 but in this paper, the influence of the undrained
shear strength and time on the regeneration factor is investigated. A relation between the quantities is proposed, which in the end may imply an economical benefit in the design of pile foundations.
1
INTRODUCTION
In Denmark, driven squared concrete piles are very commonly used. During pile
installation, the soil close to the pile surface is remoulded, and depending on the
soil, negative or excess pore-water pressures develop (see for example Tomlinson
1994; Bond & Jardine, 1991). That is, the soil that surrounds the pile will not have
the same strength immediately after the installation as it had before pile driving
took place.
The excess pore-water pressures dissipate over time, which implies that some of
the strength lost during the installation of the pile will be recreated over time. Furthermore, even though the excess pore-water pressures are dissipated the strength
of the soil and thereby the ultimate bearing capacity of a pile can increase over
time. This is due to true time effects denoted ageing. For further details on the influence of time on soil strength and ultimate bearing capacity of piles, see for example Augustesen et al. (2002); Schmertmann (1991); Bergdahl & Hult (1981);
Karlsrud & Haugen (1986); Wardle et al. (1992); Powell et al. (2003); Soderberg
(1962); Flaate (1972); Chow et al. (1998); Long et al. (1999); Chen et al. (1999);
Axelsson (2000); Fellenius et al. (1989) and Skov & Denver (1988).
NGM 2004, Foundations, piles and soil improvements
D-103
In connection with geostatic formulas used in Danish engineering practice to calculate the ultimate bearing capacity of an axially loaded pile, time (consoli-dation
and ageing effects) is only assumed to influence the calculated skin friction in clay
(DS 415, 1998). In reality, time may also play a role in connection with skin friction in sand and toe resistance in both sand and clay. See for example Axelsson
(1998); Chow et al. (1997) and Konrad & Roy (1987) for comments regarding skin
friction in sand and clay and toe resistance in clay.
In Denmark, the regeneration factor r accounts for the effects of time on the
strength of the soil surrounding the pile and thereby the ultimate bearing capacity.
Furthermore, it is only incorporated in the equation for the skin friction in clay (see
Appendix). The r-factor is the ratio between the shear strength in a given depth at a
given time after pile driving and the shear strength in the same depth before pile
driving took place. That is, since time influences the shear strength, time also influences the r-factor and thereby the bearing capacity. According to the Danish
Code of Practice for foundation engineering (DS 415, 1998) the regeneration factor
r equals 0.4 if the value of r is not more precisely specified by means of experiments.
The purpose of this paper is to propose a relation between time, shear strength and
the regeneration factor r. This can in the end imply a better estimate on r (instead
of using r = 0.4) and eventually lead to an economical benefit. The relation is based
upon a database (section 2), which is a collection of Danish cases involving static
loading tests. In sections 3 and 4, the proposed relation is described and discussed
in some details. The geostatic formulas used in Danish engineering practice are
mentioned in the appendix.
2
DATABASE
The cases, and thereby the static loading tests from which the relation between
time, the regeneration factor, and undrained shear strength is investigated, are
listed in Table 1.
As indicated in Table 1, 7 cases are at present time included in the database. In total 12 piles have been subjected to static compression tests and 1 of the them has
been tested more than ones. All the piles are squared concrete piles. The side
length varies between 0.2m and 0.4m whereas the embedded length varies between
approximately 8m and 31m. Furthermore, the piles are located onshore and the
thickness of the clay layers varies at the different locations. In connection with the
static loading tests all piles did not fail and the time duration between testing and
pile driving lies in the interval 13 – 11600 days. In addition, one of the tests was
performed as a Constant Rate of Penetration test (Aalborg H. for the 0.3 × 0.3m
pile) and the others as tests with stepwise increase in load. The influence of testing
procedure in connection with static loading tests on the stress-strain curve for the
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NGM 2004, Foundations, piles and soil improvements
pile and the soil that surrounds is not taken into account. For details on this subject
for piles located in clay, see Bergdahl & Hult (1981).
Table 1
Case
Overview of the cases used. # piles and # tests denote the total number
of piles and the number of tests performed on each pile, respectively.
The column “soil” shows the total length of the part of the pile that is
located in clay in percentage of the total embedded length. Furthermore, the type of soil that surrounds the tip is indicated. Failure,
Comp./Tension and time state if failure occurred during testing, if the
pile was loaded in compression or tension and the time between pile
driving and testing, respectively. Clay covers soil types with marked
cohesive tendencies.
# piles/
# tests
Cross
Section
[m]
Embedded
length
[m]
Soil
[% Clay/
Tip]
Failure
Yes
Yes
No
No
No
No
No
Comp./
Tension
[C or T]
Time
[days]
3/1 or 2
0.2 × 0.2
12.0 – 13.6
50/sand
91/clay
46/sand
Fynsværket
2/1
0.3 × 0.3
25.9 – 26.4
84/clay
Fynsværket
2/1
0.35 × 0.35 25.8 – 29.0
84/clay
Hanstholm
1/1
0.3 × 0.3
11.4 – 16.8
39/sand
No
C
13
Aalborg H.
1/1
0.3 × 0.3
30.8
37/gravel
Yes
C
15
Aalborg H.
1/1
0.35 × 0.35
28.0
41/gravel
Yes
C
20
Århus Ø.
2/1
0.4 × 0.4
8.3 – 15.5
63-80/clay
No
No
C
29
79
Budolfi
3
C
C
C
22
14/9399
18
26
27
11600
11600
REGENERATION FACTOR AS FUNCTION OF TIME AND UNDRAINED
SHEAR STRENGTH
In this section a relation between the regeneration factor r, time t, and undrained
shear strength cu (determined by means of field vane test), is discussed. The relation is based on experimental load-settlement curves associated with the cases in
the database and an approach to reproduce load-settlement curves proposed by
Vijayvergiya (1977). First, the assumptions applied in this study related to the
Vijayvergiya method are discussed.
3.1 Vijayvergiya method for reproducing measured load-settlement curves
Vijayvergiya (1977) proposes a method to reproduce load-settlement curves for
piles by means of equations describing the mobilization of the skin friction and the
NGM 2004, Foundations, piles and soil improvements
D-105
base resistance. The method is combined with the geostatic formulas given in
DS 415 (1998). Furthermore, the formulas are used to calculate the maximum skin
friction and the base resistance. The method is also capable of extending the loadsettlement curves for piles, which have not been loaded to failure in connection
with a static load test and thereby determine the ultimate resistance.
Vijayvergiya (1977) states that the maximum skin friction and the base resistance
are mobilized at a critical movement zc of the pile skin and the pile base, respectively. The skin friction is fully mobilized at a critical movement zc,skin of 0.2 – 0.3
inches (Vijayvergiya, 1977), whereas Tomlinson (1994) states that zc,skin is 0.3 –
1.0% of the pile diameter. In this analysis zc,skin = 4mm is used, which is approximately the average of the values stated above for piles normally used in Denmark.
In this study it is assumed that the base resistance is fully mobilized at a critical
movement zc,base equal to 5% of the pile diameter. For comparison, Vijayvergiya (1977) and Tomlinson (1994) for example postulate that zc,base = 4 – 6% and
zc,base = 10 – 20% of the pile diameter, respectively.
In DS 415 (1998) the regeneration factor r, the bearing capacity factor Nm, and the
material factor m associated with the geostatic formulas have predefined values
(see Appendix). In this study, the values of r and Nm for each layer along the pile
shaft are fitted in such a way that the calculated load-settlement curve for a given
pile by using Vijayvergiya’s method is identical to the load-settlement curve obtained by a static load test performed on the same pile. In this way, different values
for r and Nm are obtained for each layer along the pile and the relation between
undrained shear strength of the different layers surrounding the pile, the regeneration factor, and time, can be studied.
Vijayvergiya’s method has been demonstrated by Jensen (2004); Sørensen & Jensen (1996) and Mosher & Dawkins (2000).
3.2 Regeneration factor vs. Undrained shear strength and time.
By using Vijayvergiya’s method on every case mentioned in Table 1, it has been
possible to investigate the influence of time and undrained shear strength on the
regeneration factor. The results are illustrated in Figure 1.
In Figure 1, every single curve represents the fitted regeneration factor for every
single cohesive soil layer surrounding the pile as a function of the undrained shear
strength for that given layer. That is, the accentuated points (points marked with ▲,
■, x or ○) on each curve symbolize the regeneration factor for a given layer with a
certain undrained shear strength at a given time after installation of a given pile.
Furthermore, the results are divided into time categories depending on the time duration between pile driving and testing. For example, in the case “Budolfi” the
undrained shear strengths for the cohesive soil layers surrounding one of the piles
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NGM 2004, Foundations, piles and soil improvements
are 25, 110, 120, 140 and 225kPa, respectively. The corresponding regeneration
factors (estimated by reproducing the load-settlement curve for the pile by means
of Vijayvergiya’s method) are 1.10, 0.92, 0.90, 0.88 and 0.85. The pile was tested
statically 9399 days after the installation.
1.25
13 days
14 days
Regeneration Factor.
1.00
15 days
18 days
0.75
20 days
22 days
0.50
26 days
27 days
0.25
29 days
79 days
9 399 days
0.00
0
100
200
300
400
500
600
700
800
11 600 days
2
Undrained Shear Strength [kN/m ]
Figure 1
The regeneration factor vs. the undrained shear strength. Time is divided into t ≤ 2 weeks (▲), 2 weeks < t ≤ 3 weeks (■), 3 weeks < t ≤ 4
weeks (x), t > 4 weeks (○). (After Jensen, 2004)
For each time interval the results presented in Figure 1 have been fitted with a
curve and depicted in Figure 2. It appears that the curves for the different time intervals are similar in shape. Furthermore, Figure 1 and Figure 2 indicate that the
regeneration factor increases when the undrained shear strength decreases. In addition, it seems like the regeneration factor increases with time. If the pile is left untouched for 4 weeks or more, the regeneration factor will exceed 0.4 for undrained
shear strengths below 714 kPa. In that case r = 0.4 as proposed by DS 415 (1998)
may be too conservative.
The tendencies illustrated in Figure 2 can approximately be described by the following equation:
 t 
r = 2.31c u -0.26 
 , t ≤ 70 days
(1)
t

 ref 
where t is time in days, cu is the undrained shear strength determined by means of
field vane test, and tref is the reference time. The reference time tref is found to be
NGM 2004, Foundations, piles and soil improvements
D-107
70 days in order to get the best fit. The curves in Figure 2 do almost coincide with
curves based on Eq.(1) for t = 14, 21, 28 and 70 days, respectively.
Regeneration factor
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
100
200
300
400
500
600
700
800
2
Undrained Shear Strength [kN/m ]
Less than 2 weeks
3 to 4 weeks
Figure 2
4
2 to 3 weeks
More than 4 weeks
The regeneration factor as a function of undrained shear strength
and time. (After Jensen, 2004)
DISCUSSION
The above mentioned results should be viewed upon as preliminary investigations
on how to use existing data to develop a relation between time, strength and capacity of a pile. In the future, more tests should be subjected to such an analysis in
order to calibrate and verify the model. If it turns out that the relation described by
Eq.(1) is able to describe the regeneration factor as a function of time, it may imply
an economical benefit if the piles can be left untouched for more than 4 weeks.
Some uncertainties and limitations are associated with the analysis of the cases in
Table 1. First, the regeneration factor includes effects of pore pressure dissipation
and “true” time effects. Since the drainage conditions for the soils associated with
the different cases are not the same, the magnitude of the regeneration factor will
vary from case to case even though the dimensions of the piles, the time for testing,
and the undrained shear strengths of the layers considered, are the same. Secondly,
failure did not occur in all the tests associated with the cases in Table 1. Therefore,
some uncertainty is connected to the reproduction of these load-settlement curves
and thereby the estimation of the regeneration factor. In addition, in the analyses it
is chosen that the skin friction and the base resistance for every pile segment are
fully mobilized corresponding to deformations equal to 4mm and 5% of the pile
diameter, respectively (section 3.1). It can be discussed whether these values are
“correct”. It seems like the values of the critical deformations do not affect the
magnitude of the regeneration factor for the different cohesive soil layers. Thirdly,
piles driven within close distance of the tested pile may influence the regeneration
factor. This has not been taken into account, but it could be the case in connection
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NGM 2004, Foundations, piles and soil improvements
with “Fynsværket”, where the distance between the test piles and the surrounding
piles are approximately 1.6m. As mentioned earlier, the type of test (Constant Rate
of Penetration or tests with stepwise increment in load) influences the loadsettlement curve and thereby the regeneration factor. It should also be mentioned
that Eq.(1) is based on undrained shear strengths measured by field vane test. At
last, pore pressures were not measured during driving, i.e. whether negative or excess pore pressures were present during driving is not known. This might also affect the magnitude of the regeneration factor at a given time after pile driving and
thereby Eq.(1).
5
CONCLUSION
This paper deals with the influence of time and undrained shear strength on the regeneration factor, which is the quantity in connection with Danish engineering
practice that accounts for the effects of time on the bearing capacity of an axially
loaded pile. 7 cases (13 static pile load tests) have been investigated by means of
the approach by Vijayvergiya (1977) and the geostatic formulas used in Danish
engineering practice. A relation (Eq. (1)) between time, undrained shear strength
and the regeneration factor has been found. If a pile is left untouched for approximately 4 weeks after pile driving, it seems like the Danish Code of Practice for
foundation engineering (DS 415, 1998) are to conservative compared to the relation (Eq.(1) and Fig. 2) proposed in this paper regarding the magnitude of the regeneration factor. That is, the proposed relation may imply an economical benefit
in the design of pile foundations.
ACKNOWLEDGEMENT
The Authors would like to thank all those who provided data from their archives:
Per Aarsleff A/S, Rambøll, COWI A/S and Carl Bro.
APPENDIX
In Denmark the bearing capacity of a single axially loaded pile can be determined
by means of geostatic formulas as given in DS 415 (1998). The characteristic value
of the total bearing capacity Rck is calculated as the sum of the skin friction Rsk and
the toe resistance Rbk:
R ck =R bk +R sk
(2)
The characteristic value of the skin friction Rsk is calculated by means of empirical
equations:
NGM 2004, Foundations, piles and soil improvements
D-109
n
R sk = ∑ q sik Asi ⇒ q sik =
i=1
1
mrc u
1.5
for cohesion soil
(3)
1
N m q'm for cohesionless soil
1.5
where qsik is the characteristic value of the skin friction per unit area in the ith
layer, Asi is the pile skin area in the ith layer, m is a material factor, r is the regeneration factor, cu is the undrained shear strength, Nm is a bearing capacity factor,
and q’m is the effective vertical stress at the middle of the ith layer.
qsik =
The characteristic value of the toe resistance Rbk is:
1
R bk =q bk A b ⇒ q bk =
9cu for cohesion soil
(4)
1.5
where qbk is the characteristic toe resistance per unit area and Ab is the cross area of
the pile toe. In till with cohesive tendencies, the factor 9 can be increased to 18.
In cohesionless soils, it is recommended not to use the geostatic formulas to calculate the toe resistance, but to use the Danish Driving Formula.
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